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A bstract Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. The transformation under the action of asymptotic symmetries and the OPEs of the celestial CFT currents are deduced from the BMS flux algebra.

A bstract The surface charge algebra of generic asymptotically locally (A)dS 4 spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The Λ-BMS 4 charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat limit then reproduces the BMS 4 charge algebra of supertranslations and super-Lorentz transformations acting on asymptotically locally flat spacetimes. The BMS 4 surface charges represent the BMS 4 algebra without central extension at the corners of null infinity under the standard Dirac bracket, which implies that the BMS 4 flux algebra admits no non-trivial central extension.

A bstract We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.

A bstract The coadjoint representation of the BMS group in four dimensions is constructed in a formulation that covers both the sphere and the punctured plane. The structure constants are worked out for different choices of bases. The conserved current algebra of non-radiative asymptotically flat spacetimes is explicitly interpreted in these terms.

A bstract We show that the Ward identities of a Carrollian CFT stress tensor at null infinity reproduce the leading and subleading soft graviton theorems for massless scattering in the bulk. We deduce the expressions of the stress tensor components in terms of the bulk radiative modes, and these components turn out to be local at I in terms of the twistor potentials. This analysis makes the correspondence between the large-time limit of Carrollian amplitudes and the soft limit of momentum space amplitudes manifest. We then construct Carrollian CFT currents from the ascendants of the hard graviton operator, which satisfy the Lw 1+ ∞ algebra. We show that the large-time limit of their Ward identities implies an infinite tower of projected soft graviton theorems in the bulk, while their finite-time OPEs encode the collinear limit of scattering amplitudes.

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

A bstract We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary Diff( S 2 ) super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary Diff( S 2 ) super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge expressions are consistent with the leading and subleading soft graviton theorems. We contrast the leading BMS triangle structure to the mixed overleading/subleading BMS square structure.

A bstract Carrollian holography aims to express gravity in four-dimensional asymptotically flat spacetime in terms of a dual three-dimensional Carrollian CFT living at null infinity. Carrollian amplitudes are massless scattering amplitudes written in terms of asymptotic or null data at I . These position space amplitudes at I are to be re-interpreted as correlation functions in the putative dual Carrollian CFT. We derive basic results concerning tree-level Carrollian amplitudes yielding dynamical constraints on the holographic dual. We obtain surprisingly compact expressions for n -point MHV gluon and graviton amplitudes in position space at I . We discuss the UV/IR behaviours of Carrollian amplitudes and investigate their collinear limit, which allows us to define a notion of Carrollian OPE. By smearing the OPE along the generators of null infinity, we obtain the action of the celestial symmetries — namely, the S algebra for Yang-Mills theory and Lw 1+ ∞ for gravity — on the Carrollian operators. As a consistency check, we systematically relate our results with celestial amplitudes using the link between the two approaches. Finally, we initiate a direct connection between twistor space and Carrollian amplitudes.

A bstract We demonstrate that the one-loop exact subleading soft graviton theorem automatically follows from conservation of the BMS charges, provided that the hard and soft fluxes separately represent the extended BMS algebra at null infinity. This confirms that superrotations are genuine symmetries of the gravitational S -matrix beyond the semiclassical regime. In contrast with a previous proposal, the celestial stress tensor accounting for the one-loop corrections follows from the gravitational phase space analysis and does not require the addition of divergent counterterms. Moreover, we show that the symplectic form on the radiative phase space factorises into hard and soft sectors, and that the resulting canonical generators precisely coincide with the correct BMS fluxes.

A bstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.